Problem: Express this product in scientific notation: $(5.40\times 10^{-4})\times (7.00\times 10^{-2})$
Solution: Start by collecting like terms together. $= (5.40\times 7.00) \times (10^{-4}\times 10^{-2})$ When multiplying exponents with the same base, add the powers together. $= 37.8 \times 10^{-4\,+\,-2}$ $= 37.8 \times 10^{-6}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $37.8$ is the same as $3.780 \times 10$ $ = {3.780 \times 10} \times 10^{-6} $ $= 3.780\times 10^{-5}$